Infinity Hotel

Imagine a hotel 

with an infinite amount of rooms

an infinite amount of guests

and no vacancy.

Now imagine a bus load of 

(you guessed it) 

infinite people 

arriving at the highly reputed Infinity Hotel. 

The dedicated hotel manager 

fears not.

He requests that each guest 

move from their current room 

to their room number 

doubled. 

So the guest in room one moves to room two, 

the guest in room thirteen moves to room twenty-six. 

This empties all of the odd number of rooms 

and allows the bus full 

of infinitely many people 

to occupy the oddly infinite rooms.  

Thought experiment adopted from David Hilbert.